{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:31:23Z","timestamp":1777447883312,"version":"3.51.4"},"reference-count":44,"publisher":"SAGE Publications","issue":"3-4","license":[{"start":{"date-parts":[[2017,11,3]],"date-time":"2017-11-03T00:00:00Z","timestamp":1509667200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2017,11,3]]},"abstract":"<jats:p>We shall discuss the existence of at least one weak solution and infinitely many weak solutions for a Kirchhoff-type second-order impulsive differential equation on the half-line. Our technical approach is based on variational methods. Some recent results are extended and improved. 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